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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Addendum to ``Dense subsets of the boundary of a Coxeter system''


Author: Tetsuya Hosaka
Journal: Proc. Amer. Math. Soc. 133 (2005), 3745-3747
MSC (2000): Primary 57M07, 20F65, 20F55
Published electronically: July 7, 2005
Original Article: Proc. Amer. Math. Soc. 132 (2004), 3441-3448.
MathSciNet review: 2163614
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Abstract: In this paper, we investigate boundaries of parabolic subgroups of Coxeter groups. Let $(W,S)$ be a Coxeter system and let $T$ be a subset of $S$ such that the parabolic subgroup $W_T$ is infinite. Then we show that if a certain set is quasi-dense in $W$, then $W \partial\Sigma(W_T,T)$ is dense in the boundary $\partial\Sigma(W,S)$ of the Coxeter system $(W,S)$, where $\partial\Sigma(W_T,T)$ is the boundary of $(W_T,T)$.


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Additional Information

Tetsuya Hosaka
Affiliation: Department of Mathematics, Utsunomiya University, Utsunomiya, 321-8505, Japan
Email: hosaka@cc.utsunomiya-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08307-3
PII: S 0002-9939(05)08307-3
Keywords: Boundaries of Coxeter groups
Received by editor(s): July 5, 2004
Received by editor(s) in revised form: September 12, 2004, and October 5, 2004
Published electronically: July 7, 2005
Additional Notes: The author was partly supported by the Grant-in-Aid for Scientific Research, The Ministry of Education, Culture, Sports, Science and Technology, Japan (No. 15740029).
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.